A magnetic resonance imaging device (hereinafter, referred to as MRI device) is a diagnostic imaging apparatus for medical use, which applies a high frequency magnetic field and a gradient magnetic field to a subject placed in a static magnetic field, measures signals generated from the subject by nuclear magnetic resonance, and forms an image from the signals.
In the MRI device, generally, a slice gradient magnetic field for specifying an imaging cross section and an excitation pulse (high frequency magnetic filed pulse) for exciting magnetization in the cross section are simultaneously applied, hence to obtain nuclear magnetic resonance signals (echoes) generated during the process of converging the excited magnetization. Here, in order to impart three-dimensional positional information to the magnetization, a phase encoding gradient magnetic field and a readout gradient magnetic field vertical to each other are applied to a slice gradient magnetic field and an imaging cross section, during the period from excitation to acquisition of echoes. The measured echoes are arranged in a k space with axes kx, ky, and kz, and subjected to the inverse Fourier transform to perform image reconstruction.
Each of the pixel values of the reconstructed image becomes a complex number including an absolute value and a declination (phase). A gray scale image (absolute value image) having pixel values of absolute values is an image in which density of protons (hydrogen nuclei) and relaxation time (T1, T2) are reflected, excellent in visualizing a tissue structure. On the other hand, a gray scale image (phase image) having pixel values of phase is an image which reflects a magnetic field change caused by non-uniformity of static magnetic field and difference of magnetic susceptibility between living tissues.
Recently, there has been proposed a quantitative susceptibility mapping (Quantitatively Susceptibility Mapping: QSM) method in which based on the fact that the phase images reflect difference of magnetic susceptibility between tissues, a magnetic susceptibility distribution inside a living body is estimated from the phase images. It is known that the magnetic susceptibility of the living body tissue varies depending on the amount of iron and the amount of oxygen inside vein. A variation of the magnetic susceptibility provides useful information for diagnosis of neurodegenerative diseases and stroke.
For example, in the patients of Alzheimer's disease, one of the neurodegenerative diseases, it is known that according to the progress of the disease, iron deposition in plural tissues in a brain such as a tissue called putamen is increased, resulting in increasing the magnetic susceptibility. Therefore, if magnetic susceptibility of these tissues can be measured, it is expected that the objective information about the degree of the progress in the Alzheimer's disease can be obtained. Here, a magnetic susceptibility of a tissue is defined by the average magnetic susceptibility value in ROI (Region of Interest) set at arbitrary size within a target tissue.
In order to estimate a magnetic susceptibility distribution in a brain, a relational expression of a phase distribution φ and a magnetic susceptibility distribution χ expressed by the following formula (1) is used.
                              ϕ          ⁡                      (            r            )                          =                              -                                          γ                ⁢                                                                  ⁢                                  B                  0                                ⁢                                  τ                  TE                                                            4                ⁢                π                                              ⁢                      ∫                                          χ                ⁡                                  (                                      r                    ′                                    )                                            ⁢                                                                    3                    ⁢                                          cos                      2                                        ⁢                    α                                    -                  1                                                                                                                                        r                        ′                                            -                      r                                                                            3                                            ⁢                              d                3                            ⁢                              r                ′                                                                        (                  formula          ⁢                                          ⁢          1                )            
In the formula (1), φ(r) represents phase (rad) at a position r, γ represents magnetic rotation ratio of protons, B0 represents static magnetic field strength (T), τTE represents TE (Echo Time) (s), χ(r′) represents magnetic susceptibility (ppm) at the position r′, α is an angle made by a static magnetic field direction and a vector r′−r. However, in order to estimate a magnetic susceptibility distribution from the phase image using the formula (1), convolution integral of a right side has to be inversely solved. This is an inverse problem and a solution is not uniquely determined; therefore, an accurate magnetic susceptibility distribution cannot be uniquely estimated.
Accordingly, QSM method is used to estimate an approximate magnetic susceptibility distribution and form the image. Hereinafter, the magnetic susceptibility distribution approximately estimated based on the formula (1) and imaged is called a magnetic susceptibility image. The magnetic susceptibility image varies according to a calculation method and parameters used for calculation.
In these days, various QSM methods are proposed in order to calculate a magnetic susceptibility of tissue with high accuracy. For the above purpose, it is necessary to require a signal in a region in the vicinity of magic angle on the k space of the magnetic susceptibility image as accurate as possible. A relational expression of the phase distribution and the magnetic susceptibility distribution on the k space is expressed by the formula (2) which results from the Fourier transform of the formula (1), with the static magnetic field direction defined as a z direction.
                              Δ          ⁡                      (            k            )                          =                              (                                          1                3                            -                                                k                  z                  2                                                  k                  2                                                      )                    ·                      X            ⁡                          (              k              )                                                          (                  formula          ⁢                                          ⁢          2                )            
Where, k represents position vector on the k space, kz represents z component of the vector k, Δ represents phase distribution on the k space, and X represents magnetic susceptibility distribution on the k space.
Here, the magic angle indicates the angle of 55 degree or 135 degree with respect to the static magnetic field direction from the origin center of the k space, corresponding to the region of (⅓−kz2/k2)=0 in the formula (2).
Hereinafter, a region in the vicinity of the magic angle on the k space is defined as a magic angle region. The magic angle region is defined by a region satisfying the expression of |⅓−kz2/k2|<ath using some threshold ath. The threshold ath is defined as a magic angle threshold. It is known that in the magic angle region of the magnetic susceptibility image, noise is most increased and that magnetic susceptibility information of tissue is buried in the noise and lost. On the other hand, in a region other than the magic angle region, noise exists but the magnetic susceptibility information of tissue is not lost. Therefore, if the magnetic susceptibility information of tissue in the magic angle region of the k space can be calculated with high accuracy, magnetic susceptibility of tissue can be calculated with high accuracy.
In order to solve the above problems, recently, as a useful method, there has been proposed a method of calculating an edge image indicating the edge region of a tissue in advance and smoothing the region other than the edge in the magnetic susceptibility image by using the above image. The edge image means an image having larger pixel values in the edge region of a tissue than the pixel values in the other region. If the edge image indicating the edge region of a tissue on the magnetic susceptibility distribution can be calculated in advance, the magnetic susceptibility value corresponding to the magic angle region is smoothed by using the above, hence to reduce the background noise, which can improve the estimation accuracy in the magnetic susceptibility of tissue. Here, the background noise is defined by a standard deviation for ROI, for example, set in some region of a brain parenchyma on the magnetic susceptibility image. Of the methods using the edge image of these days, the typical ones are MEDI (Morphology enabled dipole inversion) method (Non-Patent Document 1) and HEIDI (Homogeneity Enabled Incremental Dipole Inversion) method (Non-Patent Document 2).